On the existence of the global conformal gauge in string theory

M. O. Katanaev
2021 European Physical Journal C: Particles and Fields  
AbstractThe global conformal gauge is playing the crucial role in string theory providing the basis for quantization. Its existence for two-dimensional Lorentzian metric is known locally for a long time. We prove that if a Lorentzian metric is given on a plain then the conformal gauge exists globally on the whole $${{\mathbb {R}}}^2$$ R 2 . Moreover, we prove the existence of the conformal gauge globally on the whole worldsheets represented by infinite strips with straight boundaries for open
more » ... d closed bosonic strings. The global existence of the conformal gauge on the whole plane is also proved for the positive definite Riemannian metric.
doi:10.1140/epjc/s10052-021-09399-9 fatcat:tufg2gj66zdupisvtecv5oau7e